Last train timetabling optimization and bus bridging service management in urban railway transit networks

Urban railway transit systems are not only the main source of city trips but also provide important support for city operations. In this study, we address the last train timetable optimization and bus bridging service problem in the context of urban railway transit networks. By exploiting problem-specific knowledge, we present an optimization-based approach that deals with the issue of last-train passengers being stranded at midnight by developing a last train and bus bridging coordination mixed integer linear programming (MILP) model. Due to the large problem size, an effective decomposition method is developed for solving the real-world and large-scale problems, which decomposes the original MILP into two smaller MILP models: maximizing last train connections and minimizing waiting times for rail-to-bus passengers. In addition, we prove that this decomposition method can solve the original MILP to global optimality. Finally, we apply the developed MILP models to the Vienna Subway to assess the effectiveness of the proposed approaches and conduct sensitivity analyses of the bus fleet size involved in the last train timetable optimization and bus bridging service problem.